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Question
An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is ______.
Options
`37 1^circ/2`
`52 1^circ/2`
`72 1^circ/2`
75°
Solution
An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is `underlinebb(52 1^circ/2)`.
Explanation:
Let one of interior angle be x°.
∴ Sum of two opposite interior angles = Exterior angle
∴ x° + x° = 105°
2x° = 105°
x° = `(105^circ)/2`
x° = `52 1^circ/2`
Hence, each angle of a triangle is `52 1^circ/2`.
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